Microwave Resonator Readout of an Ensemble Solid State Spin Sensor

ABSTRACT

Microwave resonator readout of the cavity-spin interaction between a spin defect center ensemble and a microwave resonator yields fidelities that are orders of magnitude higher than is possible with optical readouts. In microwave resonator readout, microwave photons probe a microwave resonator coupled to a spin defect center ensemble subjected to a physical parameter to be measured. The physical parameter shifts the spin defect centers&#39; resonances, which in turn change the dispersion and/or absorption of the microwave resonator. The microwave photons probe these dispersion and/or absorption changes, yielding a measurement with higher visibility, lower shot noise, better sensitivity, and higher signal-to-noise ratio than a comparable fluorescence measurement. In addition, microwave resonator readout enables coherent averaging of spin defect center ensembles and is compatible with spin systems other than nitrogen vacancies in diamond.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. application Ser. No.16/551,799, filed on Aug. 27, 2010, which in turn claims the prioritybenefit, under 35 U.S.C. 119(e), of U.S. Application No. 62/723,113,filed on Aug. 27, 2018. Each of these applications is incorporatedherein by reference in its entirety.

GOVERNMENT SUPPORT

This invention was made with Government support under Grant No.FA8702-15-D-0001 awarded by the U.S. Air Force. The Government hascertain rights in the invention.

BACKGROUND

Solid-state spin sensors employ spin center defects, including colorcenter defects, in a solid-state host to measure one or more physicalparameters or quantities, such as magnetic field, electric field,temperature, pressure, or the presence of an atomic, molecular, or otherhadronic species. The spin center defects are point-like defects insidethe solid-state host, such as nitrogen vacancies (NVs) in diamond, thatsense the physical quantity. Their quantum spin states can bemanipulated by optical excitation and microwave radiation, making thequantum spin states sensitive to the physical parameter(s).

A conventional solid-state spin sensor operates as follows. One or morecolor center defects within the solid-state spin sensor are illuminatedby optical excitation radiation from an optical radiation source.Illumination with the optical excitation radiation causes the colorcenter defects to emit fluorescent light, which is collected by a lightsensor. The application of the optical excitation radiation to the colorcenter defects may be accompanied by application of microwave radiationto the color center defects. In some implementations, the microwaveradiation is used to manipulate the population distribution between thequantum energy levels (quantum spin states) of the color center defects.

The optical excitation radiation and the microwave radiation may beapplied simultaneously, sequentially, or both simultaneously andsequentially. The application of the optical and microwave radiation tothe solid-state spin sensor is arranged so that information pertainingto the physical quantity to be measured is encoded in emittedfluorescent light. For example, if a diamond containing nitrogen-vacancycolor center defects is illuminated with green light (light at awavelength of 495-570 nm) and appropriate microwave radiation, thediamond may emit red fluorescent light (light at a wavelength of 630-850nm) that encodes the distribution of the spin center defect populationamong the quantum spin states. This population distribution depends inturn on the physical parameter applied to the spin center defects. Thus,the detected fluorescence represents the physical quantity experiencedby the spin center defects. When the physical parameter is a magneticfield, this fluorescence-based measurement is called an opticallydetected magnetic resonance (ODMR) measurement.

FIG. 1 shows a standard solid-state spin sensor system 100 with asolid-state spin sensor 110 (e.g., spin center defects, such as nitrogenvacancies, in a solid-state host, such as bulk diamond), microwaveradiation source 120, optical radiation source 130, photodetector 140,and processor 160 (e.g., in a computer). In operation, the microwaveradiation source 120 and optical radiation source 130 apply microwaveradiation and optical excitation radiation, respectively, to thesolid-state spin sensor 110. The microwave radiation and the opticalexcitation radiation may each be turned on or off by a correspondingswitch 122, 132, which may be controlled by the processor 160. Theprocessor 160 may also control aspects of the microwave radiation andthe optical excitation radiation, such as the power and spectralcontent.

When excited by the optical excitation radiation, the color centerdefects in the solid-state spin sensor 110 emit fluorescent light 111,which is collected and sent to the photodetector 140. Thephotodetector's output, which represents the intensity of thefluorescent light 111 impinging on the photodetector 140, is digitizedby an analog-to-digital converter 142 and sent to the processor 160. Theprocessor 160 uses the known temporal and spectral properties of theapplied microwave radiation and optical excitation radiation, along withthe intensity of the detected optical fluorescent light, to calculatethe value of the physical quantity exerted on the solid-state spinsensor 110.

SUMMARY

Unfortunately, reading out a solid-state spin sensor using fluorescentlight described above has a fundamental drawback: determining thequantum states of the spin center defects using the fluorescent lightcan be highly inefficient. With fluorescence-based readout, mostinformation about the physical parameter being measured (which isencoded in the quantum states of the spin center defects) is lost in theprocess of reading out the quantum states. The amount of informationlost during readout is quantified by the readout fidelity F. For F=1, noinformation is lost, and the readout fidelity cannot be improved beyondthe spin projection limit. For a readout fidelity of F=0.1, 90% ofinformation is lost. For a readout fidelity of F=0.01, 99% ofinformation is lost. Readout fidelities for solid state spin sensorsemploying the fluorescence-based readout vary from F=0.0002 to F=0.013,indicating an information loss of 98.7% at best.

Readout fidelity also affects measurement time. Generally, the time ittakes a solid-state spin sensor to achieve a given signal-to-noise ratio(SNR) is proportional to F², which means that smaller fidelitiestranslate to longer measurement times for a given SNR. In other words,the measurement time to achieve a given SNR scales as 1/F². This makesthe low readout fidelities (F<<1) of fluorescence-basedspin-center-defect measurements highly disadvantageous for measuringtransient physical quantities with relatively high SNR.

In contrast, an inventive solid-state spin sensor system can operatewith a readout fidelity approaching F=1 using a microwave resonatorreadout technique. This readout fidelity is approximately 100 timesbetter than the readout fidelity for optical readout, which translatesto a 100-fold increase in SNR and a 10,000-fold reduction in readouttime to achieve a given SNR. To achieve this readout fidelity, aninventive solid-state spin sensor system determines the quantum statesof the spin center defects by examining the characteristics of microwaveradiation that interacts with the solid-state spin sensor. Theinteraction of the input microwave radiation with the spin centerdefects is enhanced by the use of a resonant microwave cavity. For asolid-state spin sensor based on nitrogen vacancies (NVs) in diamond,this microwave resonator readout can be used to determine themagnetic-field dependent Zeeman resonances. By determining the locationof the magnetic-field dependent Zeeman resonances, the inventivesolid-state spin sensor can function as a magnetometer. Such amagnetometer can be used for applications in bio-sensing, neuroscience,geo-surveying, all-magnetic navigation, magnetic anomaly detection andother applications.

An inventive sensor system may include a microwave resonator, asolid-state host electromagnetically coupled to the microwave resonatorand containing spin defect centers, a microwave radiation source inelectromagnetic communication with the microwave resonator and the spindefect centers, and a detector in electromagnetic communication with themicrowave resonator and the spin defect centers. In operation, themicrowave radiation source applies microwave radiation to the microwaveresonator and the spin defect centers. The microwave resonator enhancesthe interaction between the microwave radiation and the spin defectcenters. And the detector measures an amplitude and/or a phase of themicrowave radiation exiting the microwave resonator after interactingwith the spin defect centers.

The detector may be configured to sense a change in the amplitude and/orthe phase of the microwave radiation in response to a shift in resonantfrequencies of the spin defect centers caused by a physical parameter,such as a magnetic field, applied to the spin defect centers. Thedetector can be implemented as a homodyne sensor with a reference arm.The detector can also be implemented as a heterodyne detector configuredto encode information, at a heterodyne frequency, about a physicalparameter that shifts resonance frequencies of the spin defect centers.

The sensor system may also include an optical excitation source (e.g., alaser), in optical communication with the spin defect centers, to excitethe spin defect centers to a desired quantum state.

The sensor system can also include a processor, operably coupled to thedetector, to determine a physical parameter experienced by the spindefect centers based on the amplitude and/or the phase of the microwaveradiation. The microwave radiation source can vary the microwaveradiation based on the physical parameter determined by the processor.And the processor can determine quantum states of the spin defectcenters based on the amplitude and/or phase of the microwave radiation.

In some cases, the sensor system includes an actuator, operably coupledto the microwave resonator, to vary a resonant frequency of themicrowave resonator. The actuator may include a piezo-electric element,varactor, tunable capacitor, or switchable capacitor bank. The actuatorcan change the resonant frequency of the microwave resonator by varyinga capacitance or an inductance. Applying multiple tones to the actuatorcan cause the microwave resonator to be resonant at multiple frequenciessimultaneously. For example, the actuator may comprise a dynamicallycontrolled capacitance configured to allow the microwave resonator to beresonant at multiple frequencies simultaneously.

Microwave resonator readout can be used to measure a physical parameterwith a microwave resonator containing a solid-state host. Spin defectcenters in the solid-state host are subjected to the physical parameter,which causes a shift in resonance frequencies of the spin defect centerswith respect to a resonance frequency of the microwave resonator. Amicrowave waveform probes the shift in the resonance frequencies of thespin defect centers with respect to the resonance frequency of themicrowave resonator. A detector measures the microwave waveformtransmitted and/or reflected from the microwave resonator and the spindefect centers. An amplitude and/or a direction of the physicalparameter can be determined from the microwave waveform transmittedand/or reflected from the microwave resonator and the spin defectcenters.

Measuring the microwave waveform can include measuring in-phase andquadrature components of the microwave waveform. In some cases,measuring the microwave waveform comprises sensing the shift in theresonance frequencies of the spin defect centers with respect to theresonance frequency of the microwave resonator with a contrast ratio ofat least 95%. Likewise, determining the amplitude and/or the directionof the physical parameter comprises measuring the physical parameterwith a readout fidelity of at least 0.1.

If desired, microwave resonator readout can be implement in a magneticfield sensor that includes a resonant circuit, a microwave source inelectromagnetic communication with the resonant circuit, a microwavedetector in electromagnetic communication with the microwave resonator,and a processor operably coupled to the microwave detector. The resonantcircuit includes a microwave resonator and a solid-state host inproximity to the microwave resonator. This solid-state host has spindefect centers that shift a resonance frequency of the microwaveresonator in response to an external magnetic field, which may change apopulation distribution of the spin defect centers among differentquantum states. The microwave source probes the resonance frequency ofthe microwave resonator with microwave radiation, and the microwavedetector detects the microwave radiation that probes the resonancefrequency of the microwave resonator. The processor determines amagnitude and/or a direction of the magnetic field based on themicrowave radiation detected by the detector.

In some cases, the microwave detector is configured to detect in-phaseand quadrature components of the microwave radiation.

The magnetic field sensor may also include locking circuitry, operablycoupled to the microwave source and the microwave detector, to lock aspectral component of the microwave radiation to the resonance frequencyof the microwave resonator.

BRIEF DESCRIPTIONS OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIG. 1 shows a typical standard solid-state spin sensor with opticalreadout.

FIG. 2A illustrates optical readout with a solid-state spin sensor.

FIG. 2B illustrates microwave resonator readout with a solid-state spinsensor.

FIG. 3A shows an inventive solid-state spin sensor system with microwaveresonator readout.

FIG. 3B shows the microwave resonator and solid-state spin sensor ofFIG. 3A in greater detail.

FIG. 3C is a plot of unloaded quality factor (Q; left axis) andpeak-to-peak frequency shift (right axis) versus varactor position forthe microwave resonator of FIG. 3B.

FIG. 4A illustrates quantum spin state transitions for spin defectcenters in a solid-state spin sensor with microwave resonator readout.

FIG. 4B shows the spin center defect microwave resonances by themselves(top) and the effect of the spins on the microwave resonator qualityfactor (bottom) for a solid-state spin sensor with microwave resonatorreadout.

FIG. 4C illustrates input coupling, with voltage reflection coefficientF, and output coupling with voltage transmission coefficient T formicrowave radiation probing the quantum spin states of spin defectcenters in a solid-state spin sensor in a microwave cavity.

FIG. 5 illustrates an eigenfrequency simulation of a solid-state spinsensor (solid, diamond-shaped outline) in a cavity formed by twodielectric microwave resonators (dashed lines), with arrows showing the2D vector field distribution.

FIG. 6 is a plot of a microwave resonator readout signal (right axis)and superimposed optically detected magnetic resonance (ODMR) signal(left axis) as a function of applied magnetic field.

FIG. 7 shows transmission (T) data (left column) and reflection (F) data(right column) for simulated (top row) and experimental (bottom row)microwave resonator readout signals from an inventive solid-state spinsensor.

FIG. 8 is a plot of the microwave resonator readout signal from aninventive solid-state spin sensor reflected into a 50Ω impedance atdifferent microwave powers.

FIG. 9 is a plot of sensitivity versus frequency for a magneticallysensitive channel (upper trace) and a magnetically insensitive channel(lower trace) of an inventive solid-state spin sensor.

DETAILED DESCRIPTION

An inventive solid-state spin sensor system encodes a physical quantityin the phase or amplitude of microwave radiation that has interactedwith spin center defects within a solid-state spin sensor. Encoding thephysical quantity in the phase and/or amplitude of microwave radiation,instead of optical radiation, greatly enhances the readout fidelity ofand sensitivity of bulk-ensemble solid state spin sensors to physicalparameters of interest and, as an all-electrical readout mechanism, maybe preferable to all-optical readout mechanisms. The solid-state spinsensor system is also more compatible with standard semiconductorprocess manufacturing than devices employing all-optical readoutmechanisms. And thanks to microwave resonator readout, an inventivesolid-state spin sensor system can work well with many more types ofspin defects, including almost any paramagnetic spin defect, than arecompatible with optical readout.

Differences Between Optical Readout and Microwave Resonator Readout

FIGS. 2A and 2B illustrate how microwave resonator readout differs fromoptical readout in a solid-state spin sensor. FIG. 2A illustratesconventional optical readout 200. Optical radiation 201 and microwaveradiation 203 are applied to solid-state spins 211 of color centerdefects in a crystalline host, placing the ensemble or population ofsolid-state spins 211 in a desired quantum state distribution. Aphysical parameter 205 measured by the sensor, such as magnetic field,electric field, pressure, or temperature, changes the relativepopulations in different quantum states of the solid-state spins 211.The change in the relative populations of the solid-state spins isreflected in different amounts of photoluminescence 221 emitted by thesolid-state spins 211. The changes in photoluminescence 221 can bedetected with a fidelity of about 0.01 at best.

FIG. 2B illustrates microwave resonator readout 250 of a solid-statespin sensor. Input microwave radiation 253 and optical radiation 251 areapplied to the solid-state spins 261 via a microwave resonator 263,polarizing the solid-state spins 261. The physical parameter 255 beingmeasured changes the relative populations in different quantum states(and the resonance frequencies) of the solid-state spins 261. The changein the population distribution of the solid-state spins 261 changes theresonance frequency or the quality factor of the microwave resonator263. The change in resonance frequency or quality factor produces achange in microwave radiation 271 transmitted or reflected by themicrowave resonator 263 that can be measured with a fidelity of at least0.1 (e.g., 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.75, 0.80, 0.85,0.90, 0.95, or higher). The contrast ratio for microwave resonatorreadout 250 can also be quite high, e.g., 50%, 60%, 70%, 80%, 90%, 95%,or higher.

Unlike in the optical readout 200, in the microwave resonator readout250, the change in the resonant frequencies of the solid-state spins 261is an intermediate effect; the solid-state spins 261 then change theresonant frequency and/or the quality factor of the microwave resonator,and the phase and/or amplitude of the output microwave radiation reflectthe microwave resonator's resonant frequency and/or quality factor.

A Solid-State Spin Sensor System with Microwave Resonator Readout

FIG. 3A shows a solid-state spin sensor system 300 with microwaveresonator readout. The solid-state spin sensor system 300 includes asolid-state spin sensor 310, which is a solid-state state host thatcontains an ensemble of spin center defects, in a microwave cavitydefined by a composite microwave resonator 380. Suitable solid-statespin sensors 310 include NVs and silicon vacancies in diamond,divacancies in silicon carbide, and titanium, chromium, manganese, iron,cobalt and nickel defects in sapphire, nickel and cobalt in magnesiumoxide. An actuator 382 tunes the resonance frequency of the compositemicrowave resonator 380. An optional bias magnet 314 applies an optionalbias magnetic field to the spin center defects in the solid-state spinsensor 310, splitting the defects' microwave resonances. And an optionaltest coil 318 can be used to apply a known time-varying magnetic fieldto the solid-state spin sensor 310 for testing or calibrating thesolid-state spin sensor system 300.

The system 300 includes a microwave generator 320, such as a pulsepattern generator, arbitrary waveform generator, direct digitalsynthesizer, dielectric resonator oscillator, or frequency-multipliedquartz oscillator, that probes the defects' microwave resonances with aninput microwave radiation. A microwave splitter 322 coupled to theoutput of the microwave generator 320 splits the input microwaveradiation into a signal arm with a first variable attenuator 324, whichis controlled by a processor 360, and a reference arm with a phaseshifter 326 and a second variable attenuator 328, which are alsocontrolled by the processor 360 (connections to the processor 360 areomitted for clarity).

A three-port circulator 370 coupled to the first variable attenuator 324couples the input microwave radiation to the microwave cavity containingthe solid-state spin sensor 310 and receives output microwave radiationreflected from the microwave cavity. The circulator 370 couples thisoutput microwave radiation through a first low-noise amplifier (LNA) 372and first band-pass filter (BPF) 374 to an in-phase/quadrature (I/Q)mixer 378, which mixes the amplified, filtered output microwaveradiation with the copy of the input microwave radiation from thereference arm. A data acquisition (DAQ) board 342, which may include oneor more analog-to-digital converters (ADCs), receives and digitizes thein-phase and quadrature outputs from the I/Q mixer 378.

The processor 360 is coupled to the DAQ board 342 uses the digitizedin-phase and quadrature outputs to compute the physical parameter(s)measured by the system 300 (e.g., the amplitude and orientation of anexternal magnetic or electric field). The DAQ board 342 may also receiveand digitize an output microwave radiation transmitted through thecavity in addition to or instead of the reflected output microwaveradiation. This transmitted output microwave radiation is amplified by asecond LNA 352, filtered by a second BPF 354, and detected by amicrowave detector 350 coupled to the DAQ board 342. (If desired, themicrowave detector 350 can be implemented as a dual-channel detector forbalanced homodyne or heterodyne detection with a local oscillatorprovided by an appropriately phase-shifted version of the inputmicrowave radiation.)

Optional locking circuitry 362 coupled to the DAQ board 342 and themicrowave generator 320 may lock at least one spectral component(frequency tone) of the input microwave radiation to the resonancefrequency of the microwave resonator 380. The locking circuitry 362generates an error signal that represents changes in resonance frequencyor quality factor of the microwave resonator 380 caused by the physicalparameter being measured. This error signal may be used to adjust thefrequency of the input microwave radiation relative to the resonantfrequency of the microwave resonator 380. (Generally, the frequency ofthe input microwave radiation is kept within a few cavity linewidths ofthe microwave resonator's resonant frequency.) The error signal can alsodrive an actuator 382 that changes the resonant frequency of themicrowave resonator 380 as explained below. For instance, the lockingcircuitry 362 can perform the locking with a Pound-Drever-Hall lock,peak dither lock, or another technique to ensure the composite microwaveresonator 380 is resonant with one or more tones of the input microwaveradiation applied to the cavity. The tone(s) in the input microwaveradiation can then be locked to one or more magnetic resonances of thesolid-state spin sensor 310.

The system 300 may also include an optional optical radiation source,such as a pump laser 330 that emits a pump beam 331 at a wavelength of532 nm. An optional modulator 332, such as a shutter or switch, controlswhether this pump beam 331 illuminates the solid-state spin sensor 310.The system 300 can also include a photodetector 340, which is coupled tothe DAQ board 342, for measuring fluorescent light emitted by the spincenter defects in the solid-state spin sensor 310, e.g., for anauxiliary ODMR measurement.

In the system 300 of FIG. 3A, the reflection from the cavity constitutesa homodyne signal that is detected by a homodyne detector in the form ofthe I/Q mixer 378. For heterodyne detection, the signal in the referencearm or the signal interrogating the cavity (the input microwaveradiation) can be modulated with a suitable modulator (e.g., the phasemodulator 326). As a result, when the reflected signal (the outputmicrowave radiation) mixes with the signal in the reference arm, the I/Qmixer 378 produces a signal of interest encoded at the modulationfrequency. One advantage of full heterodyne detection is that byencoding the signal of interest at a modulation frequency away above DC,the measurement is much less sensitive to 1/f-type noise from themicrowave generator 320 and the I/Q mixer 378. (The transmission throughthe cavity, since there is no mixing, is not a homodyne or heterodynesystem.)

Microwave Resonator Design and Construction

FIG. 3B shows a longitudinal cross section of the composite microwaveresonator 380. The microwave resonator 380 enhances the interactionbetween the spin center defects in the solid-state spin sensor 310 andthe input microwave radiation. The solid-state spin sensor 310 sits in amicrowave cavity 381 formed by dielectric resonators 384, which aresandwiched between Teflon retaining rings 392 and 396 in a housing(aluminum lens tube 390). (The microwave cavity 381 can also be formedby a metallic loop gap resonator or insulating material plated with anelectrically conductive material, such as sapphire plated with silver.)The composite microwave resonator 380 can also be composed of planarelements and can be implemented as a split ring resonator, aquarter-wavelength resonator, a patch antenna, or any other suitablemicrowave resonator. A semi-insulating silicon carbide substrate 394supports the solid-state spin sensor 380 in the cavity 381 anddissipates heat from the solid-state spin sensor 380.

The input microwave radiation is coupled into the composite microwaveresonator 380 by inductive coupling using a wire loop 376 that sticksthrough a hole in the aluminum lens tube 390 and can be moved in threedimensions. Alternatively, the input microwave radiation can be coupledinto the composite microwave resonator 380 by capacitive coupling with awire loop, end coupling, or any other suitable method of resonatorcoupling. The pump beam 331 illuminates the solid-state spin sensor 310via a window or aperture in the aluminum lens tube 390.

If desired, an actuator 382, shown in FIG. 3B as a ring coupled to oneor more varactors (not shown), can be used to tune the resonancefrequency of the composite microwave cavity 380. Moving the ringdielectric resonator and varactor 382 toward or away from the dielectricresonators 384 shifts both the unloaded quality factor (Q) and resonancefrequency of the composite microwave resonator 380 as shown in FIG. 3C.Other suitable actuators include piezo-electric elements, tunablecapacitors, and switchable capacitor banks that tune the compositemicrowave resonator's capacitance.

The composite microwave resonator's unloaded quality factor andresonance frequency can also be shifted by changing the compositemicrowave resonator's inductance. As inductance is typically determinedby the physical location of flowing current, the inductance can bechanged by changing the geometry or distance of the path traveled by thecurrent, e.g., with a switch that switches the current between differentpaths.

Applying multiple tones to the actuator (e.g., the dynamicallycontrolled capacitance shown in FIG. 3B) can cause the microwaveresonator to be resonant at multiple frequencies simultaneously. Wheninterrogating NVs in diamond, for example, it may be desirable tointerrogate some or all of the NV resonances sequentially orsimultaneously. For ¹⁴NV, for example, there are 24 resonances thanks tothe NVs' four possible orientations in the diamond latter, two possiblespin states, and three possible hyperfine states. Shifting or sweepingthe resonant frequency of the microwave resonator 380 through these NVresonances, e.g., by applying multiple tones or a frequency chirp to theactuator, makes it possible to interrogate each NV resonanceindividually.

Microwave Resonator Readout

FIGS. 4A-4C illustrate a magnetic field measurement using microwaveresonator readout with the solid-state spin sensor system 300 of FIG.3A. The magnetic field is encoded into the population ratio of the spindefect centers' |m_(s)=+1>, |m_(s)=−1>, and |m_(s)=0> spin states(assuming the spin system is based on NVs in diamond). The pump laser330 illuminates the solid-state spin sensor 310 with the pump beam 331,which is at a wavelength of 532 nm and may be modulated in amplitude,phase, and/or frequency by the modulator 332. For example, the modulator332 may pulse the pump beam 331 on and off. The pump beam 331re-polarizes the spin defect center population; that is, it changes thedistribution of the spin center defects between the different quantumenergy levels as shown in the state diagram in FIG. 4A. In thisimplementation, the pump beam 331 pumps most of the spin center defectsinto a single quantum state (the |m_(s)=0> spin state).

The microwave generator 320 irradiates the solid-state spin sensor 310with input microwave radiation whose spectral content transfers the spincenter defect population in the solid-state spin sensor between quantumenergy levels. The input microwave radiation should have low phasenoise, as phase noise can mimic a magnetic signal. Frequency shifts ofthe cavity resonance by the magnetic signal and of the microwaveradiation due to phase noise both change the amount of microwaveradiation reflected from the cavity. It can be very hard to distinguishthese two effects, one of which is caused by the magnetic signal and oneof which is caused by phase noise. Reducing or suppressing phase noisereduces unwanted variations in the amplitude of the output microwaveradiation caused by phase noise.

The spectral content of the input microwave radiation may include one ormore frequency tones, with the same or different amplitudes, each ofwhich may be within one, five, or even ten cavity linewidths of themicrowave resonator's resonant frequency. The input microwave radiationmay be amplitude modulated, frequency modulated, phase modulated, orotherwise altered in time. Like the optional optical radiation, thisinput microwave radiation interacts with the spin center defects in thesolid-state spin sensor 310 and may change the population distributionof the spin center defects between the different quantum states.

For example, the input microwave radiation parameters (frequency andphase or any combination thereof) may be arranged so that spin centerdefects in one of the quantum states absorb some fraction of the inputmicrowave radiation. This absorption appears as a dip in the solid-statespin sensor's transmission spectrum, which is plotted in the upper tracein FIG. 4B. The transmission spectrum (upper trace in FIG. 4B) has twodips because a bias magnetic field (e.g., applied by the bias magnet 314in FIG. 3A) overlaps all the |m_(s)=+1> resonances into one resonanceand the |m_(s)=0> resonances into another resonance. This optional biasmagnetic field enhances the interaction between the NVs and themicrowave resonator 380.

The dips in the solid-state spin sensor's transmission spectrum can bealigned to the microwave resonator's resonant frequency as shown in thelower trace for FIG. 4B. In addition, the microwave resonator's freespectral range may be chosen to match or mismatch the splitting betweenthe spin center defect resonances, enabling Vernier-style measurements.When the spin defect center population is near or on resonance with themicrowave resonator as in FIG. 4B, the microwave resonator's resonancelinewidth is broadened due to resonant absorption. This causes themicrowave resonator's resonant frequency to be shifted due to scatteringand re-emission of microwave photons back into the cavity mode.

Generally, the spectral content of the input microwave radiation shouldbe within a few cavity linewidths of the microwave resonator's resonancefrequency. The microwave resonator's resonance frequency can be shiftedby the spin center defects by an amount that depends on the physicalparameter (e.g., magnetic field) applied to the spin center defects. Forexample, the microwave resonator 320 may have a resonance with a centerfrequency at 2.900 GHz and a 200 kHz linewidth. To access thisresonance, the input microwave radiation has spectral content between2.899 GHz and 2.901 GHz (within five resonance linewidths of theresonance center frequency). The spin defect centers may shift theresonance center frequency up to 300 kHz in either direction. This shiftof the resonance center frequency imparts a phase and amplitudedifference to the microwave radiation reflected from the compositeresonator 380.

FIG. 4C shows that the input microwave radiation's interaction with thesolid-state spin center 310 and the microwave resonator 380 producesreflected output microwave radiation (F) and transmitted outputmicrowave radiation (T). The difference in power between the inputmicrowave radiation and the total output microwave radiation can bearranged to depend on the number of spin center defects in the quantumstate addressed by the input microwave radiation. For example, the inputmicrowave radiation parameters (frequency, phase, or any combinationthereof) may be arranged so that spin center defects in one of thequantum states introduce a phase shift (i.e., dispersion) to the inputmicrowave radiation. Upon exiting the cavity, the output microwaveradiation has a different phase than in the absence of the spin centerdefects. The additional shift in phase imparted to the output microwaveradiation by the spin center defects corresponds to the number of spincenter defects in a particular quantum state.

The coupling loop 376 inductively couples input microwave radiation intothe microwave cavity 381; input microwave radiation that isn't coupledinto the microwave cavity 381 travels back to the circulator 370 asreflected output microwave radiation. This output microwave radiation isamplified and filtered before being detected by a microwave detector,such as a dual-channel microwave detector. Suitable dual-channelmicrowave detectors include balanced mixers, dual diode detectors (e.g.,a 90-degree hybrid coupler whose outputs are coupled to a pair ofbalanced Schottky diodes), and I/Q mixers (e.g., the I/Q mixer 380 inFIG. 3A) with the reference microwave radiation input into theradio-frequency (RF) port and the output microwave radiation input intothe local oscillator (LO) port or vice versa.

Dual-channel detection is optional but offers substantial advantagesover single-channel detection. To start, a dual-channel detector canprovide get both phase and amplitude information. Typically, theabsorption is encoded in one channel and the dispersion is encoded inthe other channel. The dispersive signal is then used as an error signalfor locking the microwave frequency locked to the cavity resonance.Dual-channel detection can also be used to suppress or cancel fixedbackground.

The outputs of the dual-channel microwave detector are passed to one ormore analog-to-digital converters (e.g., in the DAQ board 342 in FIG.3A). The analog-to-digital converters digitize the outputs of thedual-channel microwave detectors and send the results to a computer(e.g., a processor in or coupled to the DAQ board 342). The computeruses the digitized outputs of the dual-channel microwave detector tocompute the value of the physical parameter to be measured using thedigitized outputs of the dual channel detector. For example, if thedual-channel microwave detector is an I/Q mixer, the outputs of thedual-channel microwave detector are in-phase and quadrature signals thatallow the computation of the amplitude and phase differences between thereference microwave radiation and the output microwave radiation. Fromeither the amplitude or phase or amplitude and phase, the computer candetermine the value of the physical parameter to be measured.

The processor 360 may also use the digitized outputs of the dual channelmicrowave detector to modulate, adjust, or otherwise control the inputmicrowave radiation or the optical excitation radiation. For instance,the processor 360 may actuate the pump laser 330, modulator 332,microwave generator 320, first variable attenuator 324, phase shifter326, or second variable attenuator 328 in FIG. 3A. These components maybe controlled to increase or maximize the sensitivity of the device,modify the performance of the device, or for any other purpose.

RLC Equivalent Circuit Model

Without being bound by any particular theory, the solid-state spinsensor and microwave resonator can be described as a classical RLCresonator with lumped element circuit components. These lumped elementcircuit components change as a result of the interactions between thespin center defects and physical parameter being measured and thecoupling between the spin center defects and the microwave resonator.This circuit characterization yields a straightforward computation ofthe reflection and transmission coefficients for microwave radiationincident on the circuit.

The coupling between the ensemble of spin center defects and themicrowave resonator can be modeled with an equivalent circuit for thecomposite device. The composite device can be described as a series RLCresonator where the coupling between the loop and microwave resonator isrepresented as a mutual inductance between the magnetic fields of theresonator mode and the coupling loop. In this circuit configuration, thespin defect center ensemble with magnetic susceptibility χ contributes anet magnetization to the flux through the microwave resonator andconsequently modifies the microwave resonator's inductance andequivalent resistance. The spin defect center ensemble susceptibility χis complex (χ=χ′−iχ″). It includes an imaginary part (χ″) that describesthe spin defect centers' absorption of microwave photons and a real part(χ′) that describes dispersion due to the spin defect centers.Separating χ into its real and imaginary components shows that theseries resistance R_(r) is modified as R′_(r)=R_(r)(1+Q₀χ″), where Q₀ isthe microwave resonator's intrinsic quality factor Q₀=ωL_(r)/R_(r), andthe series inductance L_(r) is modified as L′_(r)=L_(r)(1+χ′).

TABLE 1 (below) gives the equivalent series RLC circuit parameterscalculated using this analysis along with measured quantities of theresonant frequency (ω₀/2π), and unloaded quality factor (Q₀).

Quantity Parameter Rr .00315 Ohms L_(r) 3.75 nH C_(r) .78 pF ω₀/2π 2.94GHz Q⁰ 22000

-   -   TABLE 1: Parameters for series RLC equivalent circuit model of        the composite resonator

The series RLC equivalent circuit can be transformed into a parallel RLCequivalent circuit. TABLE 2 (below) gives the equivalent parallelcircuit parameters calculated using this analysis along with measuredquantities of the resonant frequency (ω₀/2π), and unloaded qualityfactor (Q₀).

Quantity Parameter R_(p) 1525425 Ohms L_(p) 3.75 nH C_(p) .78 pF ω₀/2π2.94 GHz Q₀ 22000

-   -   TABLE 2: Parameters for parallel RLC equivalent circuit models        of the composite resonator

Experimental Magnetic Field Spin Defect Center Microwave ResonatorMeasurements

The solid-state spin sensor system 300 shown in FIG. 3A was built andused to make simultaneous microwave resonator and ODMR measurements of amagnetic field. The solid-state spin sensor was a commerciallyavailable, natural, high-pressure high-temperature (HPHT) treateddiamond doped with nitrogen vacancies. The diamond had a particularlyhigh NV density (>10¹⁷/cm³ as measured using conventional electronparamagnetic resonance) with a linewidth of γ=8 MHz. The diamond wasmounted in a hollowed-out cavity machined into a dielectric resonator(DR) stack. The diamond, dielectric resonator stack, and silicon carbidesubstrate in FIG. 3B had an effective resonant frequency of 2.940 GHzand an unloaded quality factor (Q₀) of approximately 22,000. The inputand output coupling loops entered an aluminum shield coaxially with theDR stack and allowed for coupling into the resonator TE_(10δ) mode.

FIG. 5 shows an eigenfrequency simulation of the DR stack 384 and thesolid-state spin sensor 310 (diamond). The resonant frequency (f₀=2.940GHz) and magnetic mode spatial distribution was computed using the AnsysHigh-Frequency Structure Simulator (HFSS). The black dashed overlayshows the outline of the two dielectric resonators 384 with the diamond310 placed in the machined cavity. Arrows show the two-dimensionalvector field distribution and the shading shows the normalized magneticfield magnitude. The magnetic field of the TE_(10δ) mode resembles thatof a magnetic dipole, with the diamond sitting in a hollowed-out regionnear the field maxima.

The eigenfrequency simulation in FIG. 5 illustrates the interactionbetween the microwave radiation and the solid-state spin sensor 310. Thesolid-state spin sensor 310 is near the point of largest magnetic fieldin the microwave resonator. This increases or maximizes the interactionbetween the microwave resonator and the NV spin ensemble in the diamond,making it possible to probe the NV spin ensemble by looking at theproperties of the microwave resonator.

The NVs in the NV spin ensemble act like an absorbing medium for themicrowaves due to the NV's magnetic resonances. Due to the KramersKronig dispersion relations, the NVs also create dispersive shifts formicrowaves with frequencies near the magnetic resonances. Putdifferently, the NVs create both absorption and dispersion formicrowaves with frequencies near the magnetic resonances. This effectmay be weak but can be enhanced by using a microwave resonator byroughly the quality factor Q of the microwave resonator. (If this werean optical approach, the interaction between the NVs and the resonatorwould be increased by the cavity finesse). Once the NVs interactstrongly with the microwave resonator, the cavity center frequency andquality factor change in response to the NVs' behavior.

With the diamond at the center of the DR stack, laser access wasaccomplished by machining a cylindrical entry port through the center ofthe two resonators. Multi-watt laser excitation however causedtemperatures in the diamond to rise hundreds of degrees Kelvin, so thediamond was adhered to a 2-inch wafer of semi-insulating silicon carbide(SiC) 394 for heatsinking. This silicon carbide wafer was placed, alongwith the diamond, between the two DRs in the DR stack. A rare-earthmagnet (magnet 314 in FIG. 3A) created a DC bias field B₀≈6 G along the<100> diamond crystallographic axis, resulting in equal projection alongall four NV orientations. A test coil (coil 318 in FIG. 3A), positionedcoaxially with the rare earth magnet, allowed additional fields to beapplied, e.g., for sweeping the applied magnetic field.

The input microwave radiation was generated by a microwave generator andsplit into reference and signal arms via a directional coupler. Thesignal arm passed through a circulator that coupled microwave power intoand out of the microwave resonator. The circulator separated outputmicrowave radiation reflected by the microwave resonator from the inputmicrowave radiation. The output microwave radiation was consecutivelyfiltered, amplified, and mixed with the reference arm signal to producean in-phase and quadrature (IQ) signal at DC. The output microwaveradiation transmitted by the microwave resonator was read directly fromthe microwave resonator and digitized after an amplification stage. Themicrowave resonator readout signal was obtained by fixing the frequencyof the input microwave radiation to be on-resonance with the cavity andmodulating the amplitude of the bias magnetic field B₀ such that the NVZeeman sublevels swept over the cavity resonance at 2.94 GHz. Aphotodetector sensed fluorescence emitted by the NVs in the diamondsimultaneously.

FIG. 6 shows the microwave resonator readout signal (right axis) andODMR signal (left axis) as a function of the amplitude of the biasmagnetic field B₀. The NV ensemble displaced the cavity resonance as afunction of the applied bias field and gave a near-unity contrastmicrowave resonator readout signal. Imperfect isolation between ports 1and 3 of the circulator caused background microwave photons to reducethe contrast by 3%. This contrast reduction can be mitigated with ahigher isolation circulator. The ODMR signal, on the other hand, takensimultaneously and under the same conditions, yielded a contrast ofabout 5%.

Reflection and Transmission Readout

FIG. 7 shows 2D plots of the drive-cavity (δ=ω−ω₀) vs. spin-cavity(Δ=ω₀−ω_(s)) detuning taken by monitoring the reflected and transmittedoutput microwave radiation under a monotonically increasing DC biasfield (B₀). The two plots in the top row are simulations of themicrowave resonator-NV interaction using the equivalent circuit modeldescribed above and fit the data using the static susceptibility χ₀ andthe NV T₁ and T₂* as free parameters. The two plots in the bottom rowshow data taken with −56 dBm of input microwave radiation power suppliedto the microwave resonator. At this power level, the input microwaveradiation did not saturate the absorptive or the dispersive effects ofthe microwave resonator-NV interaction. Since the interaction wasproportional to the state polarization of the NV ensemble, the pumplaser power was set to 18 W at 523 nm.

The plots in FIG. 7 show that the interaction between the NV and thecavity was strongest at zero detuning, where the microwave resonator andNV ensemble have the same resonance frequency (e.g., as shown in thelower trace in FIG. 4B). The absorption and dispersion signal are veryvisible, resulting in a clear avoided crossing at zero detuning for bothtransmission and reflection.

The signal to noise ratio (SNR) using microwave resonator readout scalesas a function of the input microwave radiation power (V_(app)). Ideally,without saturation effects, the reflected signal should scale linearlywith this power. However, due to saturation of the |0>→|±1

transition, there is a power level above which increased input microwaveradiation power yields diminishing returns in the reflected signal(V_(rms)). Therefore, the input microwave power level should be chosento increase or maximize the slope of the reflected signal as a functionof the applied bias field

$\frac{dV_{refl}}{d\; B_{0}}.$

FIG. 8 shows microwave resonator readout measured into a 50Ω impedanceat different input microwave radiation power levels. The highest slopeoccurs for an input microwave radiation power level of 15 dBm. Thecurves in FIG. 8 give an expected Johnson-Nyquist noise limitedsensitivity of roughly

${\eta_{JN} \approx \frac{\sqrt{4k_{B}{TR}}}{\sqrt{2} \cdot {\max\left\lbrack \frac{{dV}_{rms}}{d\; B_{0}} \right\rbrack}}},$

where k_(B) is the Boltzmann constant, T is the system temperature (inKelvin), R is the resistance (50Ω), and B₀ is the applied magneticfield. The factor of √{square root over (2)} arises from theJohnson-Nyquist noise calculation being single-sided in frequency. For15 dBm of input microwave radiation, the Johnson-Nyquist noise limitedsensitivity is 1.08 pT/√{square root over (Hz)}.

FIG. 9 shows the solid-state spin sensor system's magnetic sensitivityfor microwave resonator readout as a function of frequency. The spectrumof the magnetically sensitive channel (upper trace) exhibits a minimumpower spectral density between 5 and 10 kHz and a sensitivity of 2.6pT/√Hz using the signal collected at 10 Hz. With a higher readoutfidelity (e.g., due to lower phase noise in the microwave source, andstronger resonator-spin-system coupling), the system's sensitivity couldreach 1 fT/√Hz or better. In comparison, the best ODMR sensitivitylevels bottom out at 1-10 pT/√Hz.

The sensitivity was measured by applying a test magnetic field thatvaried at 10 Hz and recording the output microwave radiation reflectedby the microwave resonator. The microwave resonator and NVs were tunedinto the strongly interacting regime (Δ≈0), where the slope of thedispersion signal was at its maximum, with an applied test magneticfield of approximately 1 μT at 10 Hz. This caused the microwaveresonator and NVs to experience dispersive and absorptive effects whichwere separated into the in-phase and quadrature channels of the I/Qmixer. However, due to different saturation behaviors of the dispersionand absorption signals, at 15 dBm of input microwave radiation, theabsorption signal was all but suppressed and was effectively notmagnetically sensitive. The dispersion channel remains magneticallysensitive for much higher microwave powers. Tuning the phase of thereference arm isolated the dispersion signal and adjusting the frequencyof the input microwave radiation increased the SNR of the dispersionsignal.

CONCLUSION

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize or be able toascertain, using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

1. A sensor system comprising: a microwave resonator; a solid-state hostelectromagnetically coupled to the microwave resonator and containingspin defect centers; a microwave radiation source, in electromagneticcommunication with the microwave resonator and the spin defect centers,to apply microwave radiation to the microwave resonator and the spindefect centers, the microwave resonator enhancing the interactionbetween the microwave radiation and the spin defect centers; and adetector, in electromagnetic communication with the microwave resonatorand the spin defect centers, to measure an amplitude and/or a phase ofthe microwave radiation exiting the microwave resonator afterinteracting with the spin defect centers.